Concept 6

Apply formulas correctly and track units.

Match the formula to the shape, use the right measurements, and keep units consistent.

Core Idea

The SAT provides geometry formulas on the reference sheet. Your job is to match the right formula to the shape, plug in the correct values, and make sure units are consistent throughout.

Understanding

Rule: Pick the formula first, then check the value and the units before you calculate.

  • Use radius, not diameter, when the formula asks for 𝑟.
  • Convert mixed units before you multiply.
  • Area answers end in square units; volume answers end in cubic units.

Write the formula, label each variable, and then substitute.

Step by Step

  1. Find the formula on the reference sheet (or recall it).
  2. Label each variable in the formula with the given value.
  3. Convert units if the dimensions aren't all in the same unit.
  4. Calculate, and attach the correct unit to your answer (square units for area, cubic for volume).

Misconceptions

  • Plugging diameter into a formula that requires radius.
  • Mixing inches and feet (or cm and m) without converting.
  • Reporting area in linear units or volume in square units.
Question

Worked Example

A cone has a diameter of 10 cm and a height of 12 cm. Which expression gives the volume of the cone, in cubic centimeters?

Select an answer to see the explanation